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Exact combinatorial algorithms and experiments for finding maximum k-plexes

Author

Listed:
  • Hannes Moser

    (TU Berlin)

  • Rolf Niedermeier

    (TU Berlin)

  • Manuel Sorge

    (TU Berlin)

Abstract

We propose new practical algorithms to find maximum-cardinality k-plexes in graphs. A k-plex denotes a vertex subset in a graph inducing a subgraph where every vertex has edges to all but at most k vertices in the k-plex. Cliques are 1-plexes. In analogy to the special case of finding maximum-cardinality cliques, finding maximum-cardinality k-plexes is NP-hard. Complementing previous work, we develop exact combinatorial algorithms, which are strongly based on methods from parameterized algorithmics. The experiments with our freely available implementation indicate the competitiveness of our approach, for many real-world graphs outperforming the previously used methods.

Suggested Citation

  • Hannes Moser & Rolf Niedermeier & Manuel Sorge, 2012. "Exact combinatorial algorithms and experiments for finding maximum k-plexes," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 347-373, October.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-011-9391-5
    DOI: 10.1007/s10878-011-9391-5
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    References listed on IDEAS

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    1. Laura A. Sanchis & Arun Jagota, 1996. "Some Experimental and Theoretical Results on Test Case Generators for the Maximum Clique Problem," INFORMS Journal on Computing, INFORMS, vol. 8(2), pages 87-102, May.
    2. Balabhaskar Balasundaram & Sergiy Butenko & Svyatoslav Trukhanov, 2005. "Novel Approaches for Analyzing Biological Networks," Journal of Combinatorial Optimization, Springer, vol. 10(1), pages 23-39, August.
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    Cited by:

    1. Jianhua Tu & Lidong Wu & Jing Yuan & Lei Cui, 2017. "On the vertex cover $$P_3$$ P 3 problem parameterized by treewidth," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 414-425, August.
    2. Wayne Pullan, 2021. "Local search for the maximum k-plex problem," Journal of Heuristics, Springer, vol. 27(3), pages 303-324, June.
    3. Zhang, Wenjie & Tu, Jianhua & Wu, Lidong, 2019. "A multi-start iterated greedy algorithm for the minimum weight vertex cover P3 problem," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 359-366.

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